Stars Crushed by Black Holes. III. Mild Compression of Radiative Stars by Supermassive Black Holes
Abstract

A tidal disruption event (TDE) occurs when the gravitational field of a supermassive black hole (SMBH) destroys a star. For TDEs in which the star enters deep within the tidal radius, such that the ratio of the tidal radius to the pericenter distanceβsatisfiesβ≫ 1, the star is tidally compressed and heated. It was predicted that the maximum density and temperature attained during deep TDEs scale as ∝β3and ∝β2, respectively, and nuclear detonation is triggered byβ≳ 5, but these predictions have been debated over the last four decades. We perform Newtonian smoothed-particle hydrodynamics simulations of deep TDEs between a Sun-like star and a 106MSMBH for 2 ≤β≤ 10. We find that neither the maximum density nor temperature follow the ∝β3and ∝β2scalings or, for that matter, any power-law dependence, and that the maximum-achieved density and temperature are reduced by ∼1 order of magnitude compared to past predictions. We also perform simulations in the Schwarzschild metric and find that relativistic effects modestly increase the maximum density (by a factor of ≲1.5) and induce a time lag relative to the Newtonian simulations, which is induced by time dilation. We also confirm that the time the star spends at high density and temperature is more »

Authors:
; ;
Publication Date:
NSF-PAR ID:
10379422
Journal Name:
The Astrophysical Journal
Volume:
939
Issue:
2
Page Range or eLocation-ID:
Article No. 71
ISSN:
0004-637X
Publisher:
DOI PREFIX: 10.3847
National Science Foundation
##### More Like this
1. Abstract

We develop a Newtonian model of a deep tidal disruption event (TDE), for which the pericenter distance of the star,rp, is well within the tidal radius of the black hole,rt, i.e., whenβrt/rp≫ 1. We find that shocks form forβ≳ 3, but they are weak (with Mach numbers ∼1) for allβ, and that they reach the center of the star prior to the time of maximum adiabatic compression forβ≳ 10. The maximum density and temperature reached during the TDE follow much shallower relations withβthan the previously predicted$ρmax∝β3$and$Tmax∝β2$scalings. Belowβ≃ 10, this shallower dependence occurs because the pressure gradient is dynamically significant before the pressure is comparable to the ram pressure of the free-falling gas, while aboveβ≃ 10, we find that shocks prematurely halt the compression and yield the scalings$ρmax∝β1.62$and$Tmax∝β1.12$. We find excellent agreement between our results and high-resolution simulations. Our results demonstrate that, in the Newtonian limit, the compression experienced by the star is completely independent of the mass of the black hole. We discuss our results in the context of existing (affine) models, polytropic versus non-polytropic stars, and general relativistic effects, which become important when the pericenter ofmore »

2. Abstract

Tidal disruption events (TDEs) provide a unique opportunity to probe the stellar populations around supermassive black holes (SMBHs). By combining light-curve modeling with spectral line information and knowledge about the stellar populations in the host galaxies, we are able to constrain the properties of the disrupted star for three TDEs. The TDEs in our sample have UV spectra, and measurements of the UV Niiito Ciiiline ratios enabled estimates of the nitrogen-to-carbon abundance ratios for these events. We show that the measured nitrogen line widths are consistent with originating from the disrupted stellar material dispersed by the central SMBH. We find that these nitrogen-to-carbon abundance ratios necessitate the disruption of moderately massive stars (≳1–2M). We determine that these moderately massive disruptions are overrepresented by a factor of ≳102when compared to the overall stellar population of the post-starburst galaxy hosts. This implies that SMBHs are preferentially disrupting higher mass stars, possibly due to ongoing top-heavy star formation in nuclear star clusters or to dynamical mechanisms that preferentially transport higher mass stars to their tidal radii.

3. Abstract

We present a toy model for the thermal optical/UV/X-ray emission from tidal disruption events (TDEs). Motivated by recent hydrodynamical simulations, we assume that the debris streams promptly and rapidly circularize (on the orbital period of the most tightly bound debris), generating a hot quasi-spherical pressure-supported envelope of radiusRv∼ 1014cm (photosphere radius ∼1015cm) surrounding the supermassive black hole (SMBH). As the envelope cools radiatively, it undergoes Kelvin–Helmholtz contractionRvt−1, its temperature risingTefft1/2while its total luminosity remains roughly constant; the optical luminosity decays as$νLν∝Rv2Teff∝t−3/2$. Despite this similarity to the mass fallback rate$Ṁfb∝t−5/3$, envelope heating from fallback accretion is subdominant compared to the envelope cooling luminosity except near optical peak (where they are comparable). Envelope contraction can be delayed by energy injection from accretion from the inner envelope onto the SMBH in a regulated manner, leading to a late-time flattening of the optical/X-ray light curves, similar to those observed in some TDEs. Eventually, as the envelope contracts to near the circularization radius, the SMBH accretion rate rises to its maximum, in tandem with the decreasing optical luminosity. This cooling-induced (rather than circularization-induced) delay of up to several hundred days may account for themore »

4. Abstract

The tidal disruption of stars by supermassive black holes (SMBHs) probes relativistic gravity. In the coming decade, the number of observed tidal disruption events (TDEs) will grow by several orders of magnitude, allowing statistical inferences of the properties of the SMBH and stellar populations. Here we analyze the probability distribution functions of the pericenter distances of stars that encounter an SMBH in the Schwarzschild geometry, where the results are completely analytic, and the Kerr metric. From this analysis we calculate the number of observable TDEs, defined to be those that come within the tidal radiusrtbut outside the direct capture radius (which is, in general, larger than the horizon radius). We find that relativistic effects result in a steep decline in the number of stars that have pericenter distancesrp≲ 10rg, whererg=GM/c2, and that for maximally spinning SMBHs the distribution function ofrpat such distances scales as$frp∝rp4/3$, or in terms ofβrt/rpscales asfββ−10/3. We find that spin has little effect on the TDE fraction until the very-high-mass end, where instead of being identically zero the rate is small (≲1% of the expected rate in the absence of relativistic effects). Effectively independent of spin, if the progenitorsmore »

5. Abstract The distribution of orbital energies imparted into stellar debris following the close encounter of a star with a supermassive black hole is the principal factor in determining the rate of return of debris to the black hole, and thus in determining the properties of the resulting lightcurves from such events. We present simulations of tidal disruption events for a range of β ≡ r t / r p where r p is the pericenter distance and r t the tidal radius. We perform these simulations at different spatial resolutions to determine the numerical convergence of our models. We compare simulations in which the heating due to shocks is included or excluded from the dynamics. For β ≲ 8, the simulation results are well-converged at sufficiently moderate-to-high spatial resolution, while for β ≳ 8, the breadth of the energy distribution can be grossly exaggerated by insufficient spatial resolution. We find that shock heating plays a non-negligible role only for β ≳ 4, and that typically the effect of shock heating is mild. We show that self-gravity can modify the energy distribution over time after the debris has receded to large distances for all β . Primarily, our results show thatmore »